Evaluate and simplify

Question

Given g(x) = 3/(x+2), evaluate and simplify:

g(5+h)-g(5)

--------------  =  ????

        h 

 

The answer should be -3/(49+7h). 

Please show me the steps to get this answer 

Answer 1

Hi Michelle,

 

Hopefully you see how to get to here:

 

   3              3

--------   -   ----

 (7+h)          7

--------------------

         h

 

That is what is called a complex fraction. You could get a common denominator for the fractions in the numerator, combine those fractions and then multiply the numerator by the reciprocal of the denominator.

 

My preference is to multiply the numerator and denominator of the "big" fraction by the LCD/LCM of the two "little" denominators, which would be 7(7+h).

 

The new fractions in the numerator are no longer fractions because the denominators cancel out:

 

 

  21 - 3(7+h)

-----------------

  7h(7+h)

 

Which simplifies to:

 

-3h

------------

h(49+7h)

 

The factor of h in the numerator and denominator cancel out, leaving the answer you have indicated.